Math, asked by braghav, 5 months ago

find the length of major axis minor axis length of latest rectum and eccentricity of following ellipse 9x^2 +4y^2=36

Answers

Answered by SajanJeevika
5

Solutions:-

The given is the ellipse x²/36 + y²/16 = 1.

Here,

The denominator of x²/36 is greater than the denominator of y²/16

Therefore,

the major axis is along the x - axis.

the minor axis is along the y - axis.

On comparing the given equation with x²/a² + y²/b² = 1

We obtain

a = 6 and b = 4

=> c = √a² - b²

= √(6)² - (4)²

= √36 - 16

= √20

= 2√5

Therefore,

The coordinates of the fouc are (2√5, 0) and (-2√5, 0)

The coordinates of the vertices are (6, 0) and (-6, 0).

Length of majar axis => 2a = 2 × 6 = 12

Length of minor axis => 2b = 2 × 4 = 8

Eccentricity , e = c/a

=> 2√5/6

=> √5/3

Length of Latus rectum => 2b²/a

=> 2 × 16/6

=> 16/3

Hence, the coordinates of the fouc are (2√5, 0) and (-2√5, 0), The coordinates of the vertices are (6, 0) and (-6, 0). Length of majar axis = 12. Length of minor axis = 8, Eccentricity = √5/3, And Length of Latus rectum = 16/3.

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